Agreed that it's unclear, and that the name of the style is misleading. Pummeling Style isn't Clustered Shots and it isn't Dead Shot. What's considered a "normal amount of damage" is also a bit up in the air. Where the feat fails is its lack of specificity. There's so little precedent for making multiple rolls to hit for a single attack that most rules don't even account for the possibility. So lots of room for interpretation.
That said, I'm inclined to think this works similarly to Dead Shot. Dead Shot has you make multiple attack rolls for a single attack, and has similar rules on critical hit confirmation. Anything on the target's end that's triggered on-hit would be triggered once and applied to the entire full-attack (miss chance/mirror image/etc.) In the same way that dead shot represents careful aim, pummeling style represents focusing on a single punch. Poor naming will just have to be forgiven. :)